Society naturally divides into authoritarians and liberals. The reason is, everyone starts out as authoritarian, following instruction from parents and teachers. (Authoritarian does not mean being bossy or socially dominant (SD); it means following authority.)
Later in life, upon entering adulthood, some people self-actualise, individuate, start thinking more independently, become free-thinkers. (The process is a difficult wrench because the automatic follow-the-leader instincts and peer pressure have to be wrestled with.)
People who are free-thinkers tend to let others get on with their own thing: a generally liberal attitude. Authoritarians generally stick to their chosen authority base.
Professor Bob Altemeyer devised a psychological test to measure right-wing authoritarianism (RWA),. He managed to get US politicians to take the test, the results from which are shown below, (and here, page 201). The scoring showed that the right-wing tended to cluster to their authority-bound attitudes while the left were more distributed across the spectrum, following their own ideas, however varied they were.
Autoritarian versus liberal is not the only division in politics. There is also an economic dimension. The Political Compass is a good site for finding out about this.
The Political Compass puts the terms left and right on the economic axis saying:
Our essential point is that Left and Right, although far from obsolete, are essentially a measure of economics.
However, in its origin, and still to a large extent today, I would say, left and right relate to the social authoritarian-liberal spectrum. In the French Revolution the right were the authority loyalists and the left were the ones with new ideas. There was also a respective dimension of wealth preservation and wealth redistribution though.
Wikipedia: Left-right politics
The terms "left" and "right" appeared during the French Revolution of
1789 when members of the National Assembly divided into supporters of
the king to the president's right and supporters of the revolution to
Presumably the rebels were placed on the establishment's left side, the "sinister" (sinistro) side, for nuanced effect, while the authoritarian loyalists were on the honoured right.
By contrast, in reference to the Tâo Te Ching, Chapter 31, C. Spurgeon Medhurst (trans.) writes:
The references to the right and the left will be understood when it is
remembered that in China the left is the seat of honor, the right the
lower and inferior seat.
So in China the esteem of left and right is opposite to that in the Roman and Western world, indicating no common source.